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Published on: January 13, 2026
Multi-Objective Optimization Design and Impact Protection Efficacy of Locally Reinforced P-TPMS Forehead Helmet
1School of Transportation Engineering, Nanjing Institute of Technology, Nanjing 211167, China.
Materials (Basel, Switzerland)
|June 26, 2026
Summary
This study introduces a novel Primitive-type triply periodic minimal surface (P-TPMS) helmet liner to enhance energy absorption and reduce head injury risk. The P-TPMS liner significantly lowers head injury criteria (HIC) and peak linear acceleration (PLA) compared to traditional designs.
Area of Science:
- Biomechanics
- Materials Science
- Mechanical Engineering
Background:
- Conventional helmet liners, like expanded polystyrene (EPS), face limitations in mitigating high-energy impacts, leading to potential head injuries.
- Bottom-out failure and insufficient energy absorption are critical issues in current helmet liner technology.
- Reducing the risk of skull fractures and mild traumatic brain injury (mTBI) requires advanced energy-dissipating materials.
Purpose of the Study:
- To develop and optimize a novel energy-absorbing liner for helmets to mitigate bottom-out failure and improve impact protection.
- To enhance the energy absorption capabilities of helmet liners during high-energy impacts, thereby reducing head injury risks.
- To investigate the efficacy of a locally reinforced Primitive-type triply periodic minimal surface (P-TPMS) liner in a helmet forehead region.
Main Methods:
- A finite element model of a helmet-head coupling was developed and validated against the ECE 22.06 standard drop-test methodology.
- The Box-Behnken Design (BBD) response surface methodology was employed to optimize critical design parameters: outer protective layer thickness, TPMS unit cell size, and wall thickness.
- Multi-objective optimization was used to determine ideal parameter combinations, assessing protective efficacy through head dynamic and biomechanical responses.
Main Results:
- Optimized P-TPMS liner parameters: 14.95 mm outer layer thickness, 12.23 mm unit cell size, and 3.93 mm wall thickness.
- The optimized P-TPMS liner reduced head injury criteria (HIC) by approximately 16% and peak linear acceleration (PLA) by 14% compared to EPS liners.
- Intracranial pressure and brain tissue strain were reduced below clinical injury thresholds, significantly lowering risks of skull fracture and mTBI.
Conclusions:
- The P-TPMS liner design offers superior energy dissipation through layer-by-layer buckling deformation, enhancing helmet protective efficacy.
- This advanced liner design extends impact duration and markedly improves overall helmet performance.
- Findings provide a foundation for localized heterogeneous liner designs in high-performance helmets, particularly for frontal impact conditions.

